Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
896 conjugacy classes of subgroups.
The subgroup lattice has 768 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20288854 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20285936 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20285111 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20274046 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20274036 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20274029 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20274019 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20273349 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20273323 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #20273322 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#3218 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #16811377 | C22 | 1 | 1 | yes | characteristic |
| 13 | #16811375 | — | 2 | 1 | no | — |
| 14 | #16811371 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16811370 | — | 2 | 1 | no | — |
| 16 | #16811369 | — | 2 | 1 | no | — |
| 17 | #16811367 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16811365 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16811364 | — | 2 | 1 | no | — |
| 20 | #16811363 | — | 2 | 1 | no | — |
| 21 | #16811361 | — | 2 | 1 | no | — |
| 22 | #16811173 | C22 | 1 | 1 | yes | characteristic |
| 23 | #16811170 | — | 2 | 1 | no | — |
| 24 | #16811160 | — | 2 | 1 | no | — |
| 25 | #16811157 | C22 | 1 | 1 | yes | characteristic |
| 26 | #16811151 | — | 2 | 1 | no | — |
| 27 | #16811135 | — | 2 | 1 | no | — |
| 28 | #16811132 | — | 2 | 1 | no | — |
| 29 | #16811132 | — | 2 | 1 | no | — |
| 30 | #16811029 | C22 | 1 | 2 | yes | complemented |
| 31 | #16810985 | C22 | 1 | 2 | yes | — |
| 32 | #16810985 | C22 | 1 | 2 | yes | — |
| 33 | #16810985 | C22 | 1 | 2 | yes | complemented |
| 34 | #16810975 | — | 2 | 1 | no | — |
| 35 | #16810971 | — | 2 | 1 | no | — |
| 36 | #16810953 | — | 2 | 1 | no | — |
| 37 | #16810936 | — | 2 | 1 | no | — |
| 38 | #16810915 | — | 2 | 1 | no | — |
| 39 | #16810910 | — | 2 | 1 | no | — |
| 40 | #16810680 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #16810622 | — | 2 | 1 | no | — |
| 42 | #16810622 | — | 2 | 1 | no | — |
| 43 | C4×#11719917 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #16810365 | C22 | 1 | 2 | yes | complemented |
| 45 | #16810364 | C22 | 1 | 2 | yes | complemented |
| 46 | #16810363 | C22 | 1 | 2 | yes | — |
| 47 | #16810362 | C22 | 1 | 2 | yes | — |
| 48 | #16810362 | C22 | 1 | 2 | yes | — |
| 49 | #16810362 | C22 | 1 | 2 | yes | complemented |
| 50 | C2×C4⋊Q8×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | C53×#529 | C22 | 1 | 1 | yes | characteristic |
| 52 | C53×#497 | C22 | 1 | 2 | yes | — |
| 53 | C53×#491 | C22 | 1 | 2 | yes | complemented |
| 54 | C53×#462 | — | 2 | 1 | no | — |
| 55 | C53×#461 | — | 2 | 1 | no | — |
| 56 | C53×#451 | — | 2 | 1 | no | — |
| 57 | C53×#448 | — | 2 | 1 | no | — |
| 58 | C53×#432 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | C2×#11719945 | — | 2 | 1 | no | — |
| 60 | C2×#11719945 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×#11719945 | D4 | 1 | 1 | yes | characteristic |
| 62 | C22×C4×D53 | — | 2 | 1 | no | — |
| 63 | C2×#11719917 | — | 2 | 1 | no | — |
| 64 | #13133217 | D4 | 1 | 1 | yes | characteristic |
| 65 | #13133216 | — | 2 | 1 | no | — |
| 66 | #13133214 | D4 | 1 | 1 | yes | characteristic |
| 67 | #13133213 | — | 2 | 1 | no | — |
| 68 | #13133212 | — | 2 | 1 | no | — |
| 69 | #13133212 | — | 2 | 1 | no | — |
| 70 | #13133212 | — | 2 | 1 | no | — |
| 71 | #13133211 | — | 2 | 1 | no | — |
| 72 | #13133210 | — | 2 | 1 | no | — |
| 73 | #13133209 | C23 | 1 | 1 | yes | characteristic |
| 74 | #13133208 | — | 2 | 1 | no | — |
| 75 | #13133207 | — | 2 | 1 | no | — |
| 76 | #13133206 | — | 2 | 1 | no | — |
| 77 | #13133205 | C23 | 1 | 1 | yes | characteristic |
| 78 | #13133205 | C23 | 1 | 1 | yes | characteristic |
| 79 | #13133205 | C23 | 1 | 1 | yes | characteristic |
| 80 | #13133203 | — | 2 | 1 | no | — |
| 81 | #13133203 | — | 2 | 1 | no | — |
| 82 | #13133203 | — | 2 | 1 | no | — |
| 83 | #13133202 | — | 2 | 1 | no | — |
| 84 | #13133202 | — | 2 | 1 | no | — |
| 85 | #13133202 | — | 2 | 1 | no | — |
| 86 | #13133202 | — | 2 | 1 | no | — |
| 87 | #13133202 | — | 2 | 1 | no | — |
| 88 | #13133201 | — | 2 | 1 | no | — |
| 89 | #13133201 | — | 2 | 1 | no | — |
| 90 | #13133200 | — | 2 | 1 | no | — |
| 91 | #13133199 | — | 2 | 1 | no | — |
| 92 | #13133199 | — | 2 | 1 | no | — |
| 93 | #13133199 | — | 2 | 1 | no | — |
| 94 | #13133197 | — | 2 | 1 | no | — |
| 95 | #13133197 | — | 2 | 1 | no | — |
| 96 | #13133196 | D4 | 1 | 1 | yes | characteristic |
| 97 | #13133195 | — | 2 | 1 | no | — |
| 98 | #13133195 | — | 2 | 1 | no | — |
| 99 | #13133195 | — | 2 | 1 | no | — |
| 100 | #13133194 | — | 2 | 1 | no | — |
| 101 | #13133194 | — | 2 | 1 | no | — |
| 102 | #13133193 | — | 2 | 1 | no | — |
| 103 | #13133192 | — | 2 | 1 | no | — |
| 104 | #13133192 | — | 2 | 1 | no | — |
| 105 | #13133192 | — | 2 | 1 | no | — |
| 106 | #13133192 | — | 2 | 1 | no | — |
| 107 | #13133191 | — | 2 | 1 | no | — |
| 108 | #13133191 | — | 2 | 1 | no | — |
| 109 | #13133191 | D4 | 1 | 1 | yes | characteristic |
| 110 | #13133190 | — | 2 | 1 | no | — |
| 111 | #13133190 | — | 2 | 1 | no | — |
| 112 | #13133190 | — | 2 | 1 | no | — |
| 113 | #13133190 | — | 2 | 1 | no | — |
| 114 | #13133190 | — | 2 | 1 | no | — |
| 115 | #13133189 | — | 2 | 1 | no | — |
| 116 | #13133189 | — | 2 | 1 | no | — |
| 117 | #13133188 | — | 2 | 1 | no | — |
| 118 | #13133187 | — | 2 | 1 | no | — |
| 119 | #13133187 | — | 2 | 1 | no | — |
| 120 | #13133187 | — | 2 | 1 | no | — |
| 121 | #13133187 | — | 2 | 1 | no | — |
| 122 | #13133185 | — | 2 | 1 | no | — |
| 123 | #13133185 | — | 2 | 1 | no | — |
| 124 | C4×Dic106 | D4 | 1 | 1 | yes | characteristic |
| 125 | C4×D212 | — | 2 | 1 | no | — |
| 126 | C4×D212 | — | 2 | 1 | no | — |
| 127 | C4×D212 | — | 2 | 1 | no | — |
| 128 | C4×D212 | — | 2 | 1 | no | — |
| 129 | C4×D212 | D4 | 1 | 1 | yes | characteristic |
| 130 | C4×C22⋊D53 | — | 2 | 1 | no | — |
| 131 | C4×C22⋊D53 | — | 2 | 1 | no | — |
| 132 | C4×C22⋊D53 | — | 2 | 1 | no | — |
| 133 | #13133174 | — | 2 | 1 | no | — |
| 134 | #13133174 | — | 2 | 1 | no | — |
| 135 | C42×D53 | — | 2 | 1 | no | — |
| 136 | #13133150 | — | 2 | 2 | no | — |
| 137 | #13133148 | — | 2 | 2 | no | — |
| 138 | C4⋊#88322 | — | 2 | 1 | no | — |
| 139 | #13133140 | — | 2 | 2 | no | — |
| 140 | #13133140 | — | 2 | 2 | no | — |
| 141 | #13133140 | — | 2 | 2 | no | — |
| 142 | #13133137 | — | 2 | 2 | no | — |
| 143 | #13133137 | — | 2 | 2 | no | — |
| 144 | #13133137 | — | 2 | 2 | no | — |
| 145 | C22⋊#88322 | — | 2 | 1 | no | — |
| 146 | #13133128 | C23 | 1 | 2 | yes | — |
| 147 | #13133128 | C23 | 1 | 2 | yes | — |
| 148 | C4×#88322 | — | 2 | 1 | no | — |
| 149 | C22×Q8×C53 | — | 2 | 1 | no | — |
| 150 | C2×Q16×C53 | — | 2 | 2 | no | — |
| 151 | C2×SD16×C53 | — | 2 | 2 | no | — |
| 152 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 153 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 154 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 155 | C4⋊Q8×C53 | C23 | 1 | 2 | yes | — |
| 156 | #126×C53 | — | 2 | 1 | no | — |
| 157 | #125×C53 | C23 | 1 | 1 | yes | characteristic |
| 158 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 159 | #123×C53 | — | 2 | 1 | no | — |
| 160 | C22⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 161 | #121×C53 | D4 | 1 | 1 | yes | characteristic |
| 162 | C4×Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 163 | C4×D4×C53 | — | 2 | 1 | no | — |
| 164 | C4×D4×C53 | D4 | 1 | 1 | yes | characteristic |
| 165 | #117×C53 | — | 2 | 1 | no | — |
| 166 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 167 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 168 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 169 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 170 | #103×C53 | — | 2 | 2 | no | — |
| 171 | #103×C53 | — | 2 | 2 | no | — |
| 172 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 173 | #97×C53 | C23 | 1 | 2 | yes | — |
| 174 | C23×D53 | — | 2 | 1 | no | — |
| 175 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 176 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 177 | C2×Q8×C53 | — | 8 | 2 | no | — |
| 178 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×D4×C53 | — | 2 | 1 | no | — |
| 180 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C22×C4×C53 | — | 2 | 1 | no | — |
| 182 | C22×C4×C53 | — | 4 | 1 | no | — |
| 183 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 187 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 188 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 189 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 190 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 191 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 192 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 193 | C22×Dic53 | — | 2 | 1 | no | — |
| 194 | #11719945 | — | 4 | 2 | no | — |
| 195 | #11719945 | — | 4 | 2 | no | — |
| 196 | #11719945 | — | 8 | 2 | no | — |
| 197 | C2×D212 | — | 2 | 1 | no | — |
| 198 | C2×D212 | — | 2 | 1 | no | — |
| 199 | C2×D212 | — | 2 | 1 | no | — |
| 200 | C2×D212 | — | 2 | 1 | no | — |
| 201 | C2×D212 | — | 2 | 1 | no | — |
| 202 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×D53 | — | 2 | 1 | no | — |
| 206 | C2×C4×D53 | — | 2 | 1 | no | — |
| 207 | C2×C4×D53 | — | 2 | 1 | no | — |
| 208 | C2×C4×D53 | — | 2 | 1 | no | — |
| 209 | C2×C4×D53 | — | 2 | 1 | no | — |
| 210 | C2×C4×D53 | — | 2 | 1 | no | — |
| 211 | C2×C4×D53 | — | 2 | 1 | no | — |
| 212 | C2×C4×D53 | — | 8 | 2 | no | — |
| 213 | C2×Dic106 | — | 2 | 1 | no | — |
| 214 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | Q16×C53 | — | 8 | 2 | no | — |
| 218 | SD16×C53 | — | 8 | 2 | no | — |
| 219 | C2×C8×C53 | — | 2 | 2 | no | — |
| 220 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 221 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 222 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 223 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 224 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 225 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 226 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 227 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 228 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 231 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 232 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 233 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 234 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 235 | C42×C53 | — | 2 | 1 | no | — |
| 236 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 240 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 241 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 242 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 243 | #11719921 | — | 2 | 1 | no | — |
| 244 | #11719921 | — | 2 | 1 | no | — |
| 245 | #11719921 | — | 2 | 1 | no | — |
| 246 | #11719921 | — | 2 | 1 | no | — |
| 247 | #11719921 | — | 2 | 1 | no | — |
| 248 | #11719921 | — | 2 | 1 | no | — |
| 249 | #11719921 | — | 2 | 1 | no | — |
| 250 | #11719921 | — | 2 | 1 | no | — |
| 251 | #11719921 | — | 2 | 1 | no | — |
| 252 | #11719921 | — | 2 | 1 | no | — |
| 253 | #11719921 | — | 2 | 1 | no | — |
| 254 | #11719921 | — | 2 | 1 | no | — |
| 255 | #11719921 | — | 2 | 1 | no | — |
| 256 | #11719921 | — | 2 | 1 | no | — |
| 257 | #11719921 | — | 2 | 1 | no | — |
| 258 | #11719921 | — | 2 | 1 | no | — |
| 259 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 260 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 261 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 262 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 263 | C4⋊Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 264 | C4⋊Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | #11719919 | — | 2 | 1 | no | — |
| 266 | #11719919 | — | 2 | 1 | no | — |
| 267 | #11719919 | — | 2 | 1 | no | — |
| 268 | #11719919 | — | 2 | 1 | no | — |
| 269 | #11719919 | — | 2 | 1 | no | — |
| 270 | #11719919 | — | 2 | 1 | no | — |
| 271 | #11719919 | — | 2 | 1 | no | — |
| 272 | #11719919 | — | 2 | 1 | no | — |
| 273 | C4×Dic53 | — | 2 | 1 | no | — |
| 274 | C4×Dic53 | — | 2 | 1 | no | — |
| 275 | C4×Dic53 | — | 2 | 1 | no | — |
| 276 | #11719917 | — | 4 | 2 | no | — |
| 277 | C2×#88322 | — | 2 | 2 | no | — |
| 278 | C2×#88322 | — | 2 | 2 | no | — |
| 279 | C23×C53 | — | 2 | 1 | no | — |
| 280 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 281 | C22×D53 | — | 2 | 1 | no | — |
| 282 | C22×D53 | — | 2 | 1 | no | — |
| 283 | C22×D53 | — | 2 | 1 | no | — |
| 284 | C22×D53 | — | 8 | 1 | no | — |
| 285 | C22×D53 | — | 8 | 1 | no | — |
| 286 | C22×D53 | — | 8 | 1 | no | — |
| 287 | Q8×C53 | — | 4 | 1 | no | — |
| 288 | Q8×C53 | — | 4 | 2 | no | — |
| 289 | Q8×C53 | — | 4 | 2 | no | — |
| 290 | Q8×C53 | — | 8 | 2 | no | — |
| 291 | D4×C53 | — | 4 | 1 | no | — |
| 292 | D4×C53 | — | 8 | 1 | no | — |
| 293 | C2×C4×C53 | — | 2 | 2 | no | — |
| 294 | C2×C4×C53 | — | 2 | 1 | no | — |
| 295 | C2×C4×C53 | — | 2 | 1 | no | — |
| 296 | C2×C4×C53 | — | 2 | 1 | no | — |
| 297 | C2×C4×C53 | — | 4 | 1 | no | — |
| 298 | C2×C4×C53 | — | 4 | 1 | no | — |
| 299 | C2×C4×C53 | — | 4 | 2 | no | — |
| 300 | C2×C4×C53 | — | 4 | 2 | no | — |
| 301 | C2×C4×C53 | — | 8 | 2 | no | — |
| 302 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 303 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 304 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 305 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 306 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 307 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 308 | C22⋊D53 | — | 8 | 1 | no | — |
| 309 | C22⋊D53 | — | 8 | 1 | no | — |
| 310 | C22⋊D53 | — | 8 | 1 | no | — |
| 311 | C22⋊D53 | — | 8 | 1 | no | — |
| 312 | C22⋊D53 | — | 8 | 1 | no | — |
| 313 | C22⋊D53 | — | 8 | 1 | no | — |
| 314 | C22⋊D53 | — | 8 | 1 | no | — |
| 315 | C2×Dic53 | — | 2 | 1 | no | — |
| 316 | C2×Dic53 | — | 2 | 1 | no | — |
| 317 | C2×Dic53 | — | 2 | 1 | no | — |
| 318 | C2×Dic53 | — | 2 | 1 | no | — |
| 319 | C2×Dic53 | — | 2 | 1 | no | — |
| 320 | C2×Dic53 | — | 8 | 1 | no | — |
| 321 | D212 | — | 4 | 1 | no | — |
| 322 | D212 | — | 4 | 1 | no | — |
| 323 | D212 | — | 4 | 1 | no | — |
| 324 | D212 | — | 8 | 1 | no | — |
| 325 | D212 | — | 8 | 1 | no | — |
| 326 | D212 | — | 8 | 1 | no | — |
| 327 | D212 | — | 8 | 1 | no | — |
| 328 | D212 | — | 8 | 1 | no | — |
| 329 | C4×D53 | — | 4 | 2 | no | — |
| 330 | C4×D53 | — | 4 | 2 | no | — |
| 331 | C4×D53 | — | 4 | 2 | no | — |
| 332 | C4×D53 | — | 8 | 1 | no | — |
| 333 | C4×D53 | — | 8 | 1 | no | — |
| 334 | C4×D53 | — | 8 | 1 | no | — |
| 335 | C4×D53 | — | 8 | 1 | no | — |
| 336 | Dic106 | — | 4 | 1 | no | — |
| 337 | Dic106 | — | 4 | 1 | no | — |
| 338 | Dic106 | — | 4 | 1 | no | — |
| 339 | Dic106 | — | 8 | 1 | no | — |
| 340 | C8×C53 | — | 4 | 2 | no | — |
| 341 | #88322 | — | 4 | 2 | no | — |
| 342 | #88322 | — | 4 | 2 | no | — |
| 343 | #19000 | — | 53 | 1 | no | maximal, Sylow |
| 344 | C22×C53 | — | 2 | 1 | no | — |
| 345 | C22×C53 | — | 2 | 1 | no | — |
| 346 | C22×C53 | — | 2 | 1 | no | — |
| 347 | C22×C53 | — | 4 | 1 | no | — |
| 348 | C22×C53 | — | 4 | 1 | no | — |
| 349 | C22×C53 | — | 4 | 1 | no | — |
| 350 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 351 | C2×D53 | — | 4 | 1 | no | — |
| 352 | C2×D53 | — | 4 | 1 | no | — |
| 353 | C2×D53 | — | 4 | 1 | no | — |
| 354 | C2×D53 | — | 4 | 1 | no | — |
| 355 | C2×D53 | — | 4 | 1 | no | — |
| 356 | C2×D53 | — | 4 | 1 | no | — |
| 357 | C2×D53 | — | 4 | 1 | no | — |
| 358 | C2×D53 | — | 4 | 1 | no | — |
| 359 | C2×D53 | — | 4 | 1 | no | — |
| 360 | C2×D53 | — | 8 | 4 | no | — |
| 361 | C4×C53 | — | 2 | 1 | no | — |
| 362 | C4×C53 | — | 2 | 1 | no | — |
| 363 | C4×C53 | — | 2 | 1 | no | — |
| 364 | C4×C53 | — | 2 | 1 | no | — |
| 365 | C4×C53 | — | 2 | 1 | no | — |
| 366 | C4×C53 | — | 4 | 1 | no | — |
| 367 | C4×C53 | — | 4 | 1 | no | — |
| 368 | C4×C53 | — | 4 | 1 | no | — |
| 369 | C4×C53 | — | 8 | 2 | no | — |
| 370 | C4×C53 | #455 | 1 | 2 | yes | — |
| 371 | Dic53 | — | 4 | 1 | no | — |
| 372 | Dic53 | — | 4 | 1 | no | — |
| 373 | Dic53 | — | 4 | 1 | no | — |
| 374 | Dic53 | — | 4 | 1 | no | — |
| 375 | Dic53 | — | 4 | 1 | no | — |
| 376 | #3529 | — | 53 | 1 | no | — |
| 377 | #3238 | — | 53 | 1 | no | — |
| 378 | #3218 | D53 | 1 | 1 | yes | characteristic, complemented |
| 379 | #3141 | — | 53 | 1 | no | — |
| 380 | #1664 | — | 53 | 2 | no | — |
| 381 | #1662 | — | 53 | 2 | no | — |
| 382 | #1661 | — | 53 | 2 | no | — |
| 383 | #1659 | — | 53 | 2 | no | — |
| 384 | #1536 | — | 53 | 1 | no | — |
| 385 | #1529 | — | 53 | 1 | no | — |
| 386 | #1529 | — | 53 | 1 | no | — |
| 387 | C2×C53 | — | 4 | 1 | no | — |
| 388 | C2×C53 | — | 8 | 1 | no | — |
| 389 | C2×C53 | C2×#455 | 1 | 1 | yes | characteristic |
| 390 | C2×C53 | #3021 | 1 | 1 | yes | characteristic |
| 391 | C2×C53 | #3022 | 1 | 1 | yes | characteristic |
| 392 | D53 | — | 8 | 1 | no | — |
| 393 | D53 | — | 8 | 1 | no | — |
| 394 | D53 | — | 8 | 1 | no | — |
| 395 | #563 | — | 53 | 1 | no | — |
| 396 | #563 | — | 106 | 1 | no | — |
| 397 | #562 | — | 53 | 1 | no | — |
| 398 | #562 | — | 53 | 1 | no | — |
| 399 | #562 | — | 106 | 1 | no | — |
| 400 | #562 | — | 106 | 1 | no | — |
| 401 | H(3,𝔽4) | — | 53 | 1 | no | — |
| 402 | #560 | — | 106 | 1 | no | — |
| 403 | #560 | — | 106 | 1 | no | — |
| 404 | #560 | — | 106 | 1 | no | — |
| 405 | #532 | — | 53 | 1 | no | — |
| 406 | #532 | — | 106 | 1 | no | — |
| 407 | C2×C4⋊Q8 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 408 | #529 | — | 53 | 1 | no | — |
| 409 | #529 | — | 106 | 1 | no | — |
| 410 | #529 | — | 106 | 1 | no | — |
| 411 | #529 | C2×D53 | 1 | 1 | yes | characteristic |
| 412 | #525 | — | 106 | 1 | no | — |
| 413 | #525 | — | 106 | 1 | no | — |
| 414 | #525 | — | 106 | 1 | no | — |
| 415 | #501 | — | 53 | 2 | no | — |
| 416 | #497 | C2×D53 | 1 | 2 | yes | — |
| 417 | #491 | C2×D53 | 1 | 2 | yes | complemented |
| 418 | #489 | — | 53 | 2 | no | — |
| 419 | #489 | — | 53 | 2 | no | — |
| 420 | #489 | — | 53 | 2 | no | — |
| 421 | #487 | — | 106 | 1 | no | — |
| 422 | #486 | — | 106 | 1 | no | — |
| 423 | #483 | — | 106 | 1 | no | — |
| 424 | #480 | — | 106 | 1 | no | — |
| 425 | #477 | — | 106 | 1 | no | — |
| 426 | #476 | — | 106 | 1 | no | — |
| 427 | #462 | — | 2 | 1 | no | — |
| 428 | #461 | — | 2 | 1 | no | — |
| 429 | #451 | — | 2 | 1 | no | — |
| 430 | #448 | — | 2 | 1 | no | — |
| 431 | #432 | — | 53 | 1 | no | — |
| 432 | #432 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 433 | #417 | — | 106 | 1 | no | — |
| 434 | #417 | — | 106 | 1 | no | — |
| 435 | C4×M16 | — | 53 | 1 | no | — |
| 436 | #330 | — | 53 | 2 | no | — |
| 437 | #330 | — | 53 | 2 | no | — |
| 438 | #329 | — | 53 | 2 | no | — |
| 439 | #329 | — | 53 | 2 | no | — |
| 440 | #329 | — | 53 | 2 | no | — |
| 441 | #329 | — | 53 | 2 | no | — |
| 442 | C53 | #19000 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 443 | C2×#41 | — | 53 | 1 | no | — |
| 444 | C2×#41 | — | 53 | 1 | no | — |
| 445 | C2×#41 | — | 106 | 1 | no | — |
| 446 | C22×Q8 | — | 2 | 1 | no | — |
| 447 | C23×C4 | — | 106 | 1 | no | — |
| 448 | C2×Q16 | — | 2 | 2 | no | — |
| 449 | C2×SD16 | — | 2 | 2 | no | — |
| 450 | C2×M16 | — | 106 | 1 | no | — |
| 451 | C4⋊Q8 | — | 2 | 1 | no | — |
| 452 | C4⋊Q8 | — | 2 | 1 | no | — |
| 453 | C4⋊Q8 | — | 2 | 1 | no | — |
| 454 | C4⋊Q8 | — | 53 | 1 | no | — |
| 455 | C4⋊Q8 | — | 106 | 1 | no | — |
| 456 | C4⋊Q8 | C22×D53 | 1 | 2 | yes | — |
| 457 | #127 | — | 53 | 1 | no | — |
| 458 | #127 | — | 106 | 1 | no | — |
| 459 | #126 | — | 2 | 1 | no | — |
| 460 | #126 | — | 106 | 1 | no | — |
| 461 | #126 | — | 106 | 1 | no | — |
| 462 | #126 | — | 106 | 1 | no | — |
| 463 | #126 | — | 106 | 1 | no | — |
| 464 | #126 | — | 106 | 1 | no | — |
| 465 | #125 | — | 53 | 1 | no | — |
| 466 | #125 | — | 106 | 1 | no | — |
| 467 | #125 | — | 106 | 1 | no | — |
| 468 | #125 | C22×D53 | 1 | 1 | yes | characteristic |
| 469 | #124 | — | 53 | 1 | no | — |
| 470 | #124 | — | 53 | 1 | no | — |
| 471 | #124 | — | 53 | 1 | no | — |
| 472 | #124 | — | 106 | 1 | no | — |
| 473 | #124 | — | 106 | 1 | no | — |
| 474 | #124 | — | 106 | 1 | no | — |
| 475 | #124 | — | 106 | 1 | no | — |
| 476 | #124 | C22×D53 | 1 | 1 | yes | characteristic |
| 477 | #123 | — | 2 | 1 | no | — |
| 478 | #123 | — | 106 | 1 | no | — |
| 479 | #123 | — | 106 | 1 | no | — |
| 480 | #123 | — | 106 | 1 | no | — |
| 481 | #123 | — | 106 | 1 | no | — |
| 482 | #123 | — | 106 | 1 | no | — |
| 483 | #123 | — | 106 | 1 | no | — |
| 484 | #123 | — | 106 | 1 | no | — |
| 485 | #123 | — | 106 | 1 | no | — |
| 486 | #123 | — | 106 | 1 | no | — |
| 487 | #123 | — | 106 | 1 | no | — |
| 488 | #123 | — | 106 | 1 | no | — |
| 489 | C22⋊Q8 | — | 53 | 1 | no | — |
| 490 | C22⋊Q8 | — | 106 | 1 | no | — |
| 491 | C22⋊Q8 | — | 106 | 1 | no | — |
| 492 | C22⋊Q8 | — | 106 | 1 | no | — |
| 493 | C22⋊Q8 | — | 106 | 1 | no | — |
| 494 | C22⋊Q8 | — | 106 | 1 | no | — |
| 495 | C22⋊Q8 | — | 106 | 1 | no | — |
| 496 | C22⋊Q8 | — | 106 | 1 | no | — |
| 497 | C22⋊Q8 | — | 106 | 1 | no | — |
| 498 | C22⋊Q8 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 499 | #121 | — | 53 | 1 | no | — |
| 500 | #121 | — | 106 | 1 | no | — |
| 501 | #121 | — | 106 | 1 | no | — |
| 502 | #121 | — | 106 | 1 | no | — |
| 503 | #121 | — | 106 | 1 | no | — |
| 504 | #121 | — | 106 | 1 | no | — |
| 505 | #121 | — | 106 | 1 | no | — |
| 506 | #121 | — | 106 | 1 | no | — |
| 507 | #121 | — | 106 | 1 | no | — |
| 508 | #121 | — | 106 | 1 | no | — |
| 509 | #121 | — | 106 | 1 | no | — |
| 510 | #121 | — | 106 | 1 | no | — |
| 511 | #121 | — | 106 | 1 | no | — |
| 512 | #121 | — | 106 | 1 | no | — |
| 513 | #121 | — | 106 | 1 | no | — |
| 514 | #121 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 515 | #120 | — | 106 | 1 | no | — |
| 516 | #120 | — | 106 | 1 | no | — |
| 517 | #120 | — | 106 | 1 | no | — |
| 518 | #120 | — | 106 | 1 | no | — |
| 519 | #120 | — | 106 | 1 | no | — |
| 520 | #120 | — | 106 | 1 | no | — |
| 521 | C4×Q8 | — | 53 | 1 | no | — |
| 522 | C4×Q8 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 523 | C4×D4 | — | 2 | 1 | no | — |
| 524 | C4×D4 | — | 53 | 1 | no | — |
| 525 | C4×D4 | — | 106 | 1 | no | — |
| 526 | C4×D4 | — | 106 | 1 | no | — |
| 527 | C4×D4 | — | 106 | 1 | no | — |
| 528 | C4×D4 | — | 106 | 1 | no | — |
| 529 | C4×D4 | — | 106 | 1 | no | — |
| 530 | C4×D4 | — | 106 | 1 | no | — |
| 531 | C4×D4 | — | 106 | 1 | no | — |
| 532 | C4×D4 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 533 | #117 | — | 2 | 1 | no | — |
| 534 | #117 | — | 106 | 1 | no | — |
| 535 | #117 | — | 106 | 1 | no | — |
| 536 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 537 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 538 | C2×C42 | — | 106 | 1 | no | — |
| 539 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 540 | #107 | — | 106 | 2 | no | — |
| 541 | #106 | — | 106 | 2 | no | — |
| 542 | C4⋊C8 | — | 2 | 1 | no | — |
| 543 | C4⋊C8 | — | 106 | 1 | no | — |
| 544 | #103 | — | 2 | 2 | no | — |
| 545 | #103 | — | 2 | 2 | no | — |
| 546 | #103 | — | 106 | 2 | no | — |
| 547 | #103 | — | 106 | 2 | no | — |
| 548 | #103 | — | 106 | 2 | no | — |
| 549 | #102 | — | 106 | 2 | no | — |
| 550 | #102 | — | 106 | 2 | no | — |
| 551 | #102 | — | 106 | 2 | no | — |
| 552 | C22⋊C8 | — | 2 | 1 | no | — |
| 553 | C22⋊C8 | — | 106 | 1 | no | — |
| 554 | #97 | — | 53 | 2 | no | — |
| 555 | #97 | — | 53 | 2 | no | — |
| 556 | #97 | C22×D53 | 1 | 2 | yes | — |
| 557 | C4×C8 | — | 106 | 1 | no | — |
| 558 | C24 | — | 106 | 1 | no | — |
| 559 | #41 | — | 424 | 2 | no | — |
| 560 | #41 | — | 212 | 2 | no | — |
| 561 | #41 | — | 212 | 2 | no | — |
| 562 | C2×Q8 | — | 2 | 2 | no | — |
| 563 | C2×Q8 | — | 4 | 1 | no | — |
| 564 | C2×Q8 | — | 8 | 2 | no | — |
| 565 | C2×Q8 | — | 53 | 1 | no | — |
| 566 | C2×Q8 | — | 53 | 1 | no | — |
| 567 | C2×Q8 | — | 53 | 1 | no | — |
| 568 | C2×Q8 | — | 106 | 1 | no | — |
| 569 | C2×Q8 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 570 | C2×D4 | — | 2 | 1 | no | — |
| 571 | C2×D4 | — | 53 | 1 | no | — |
| 572 | C2×D4 | — | 53 | 1 | no | — |
| 573 | C2×D4 | — | 53 | 1 | no | — |
| 574 | C2×D4 | — | 106 | 1 | no | — |
| 575 | C2×D4 | — | 106 | 1 | no | — |
| 576 | C2×D4 | — | 106 | 1 | no | — |
| 577 | C2×D4 | — | 106 | 1 | no | — |
| 578 | C2×D4 | — | 106 | 1 | no | — |
| 579 | C2×D4 | — | 106 | 1 | no | — |
| 580 | C2×D4 | — | 106 | 1 | no | — |
| 581 | C2×D4 | — | 106 | 1 | no | — |
| 582 | C2×D4 | — | 106 | 1 | no | — |
| 583 | C2×D4 | — | 106 | 1 | no | — |
| 584 | C2×D4 | — | 106 | 1 | no | — |
| 585 | C2×D4 | — | 106 | 1 | no | — |
| 586 | C2×D4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 587 | C22×C4 | — | 2 | 1 | no | — |
| 588 | C22×C4 | — | 4 | 1 | no | — |
| 589 | C22×C4 | — | 106 | 1 | no | — |
| 590 | C22×C4 | — | 106 | 1 | no | — |
| 591 | C22×C4 | — | 106 | 1 | no | — |
| 592 | C22×C4 | — | 106 | 1 | no | — |
| 593 | C22×C4 | — | 106 | 1 | no | — |
| 594 | C22×C4 | — | 106 | 1 | no | — |
| 595 | C22×C4 | — | 106 | 1 | no | — |
| 596 | C22×C4 | — | 106 | 1 | no | — |
| 597 | C22×C4 | — | 424 | 2 | no | — |
| 598 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 599 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 600 | C22×C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 601 | Q16 | — | 8 | 2 | no | — |
| 602 | SD16 | — | 8 | 2 | no | — |
| 603 | M16 | — | 212 | 2 | no | — |
| 604 | C2×C8 | — | 2 | 2 | no | — |
| 605 | C2×C8 | — | 106 | 2 | no | — |
| 606 | C2×C8 | — | 106 | 2 | no | — |
| 607 | C4⋊C4 | — | 2 | 1 | no | — |
| 608 | C4⋊C4 | — | 2 | 1 | no | — |
| 609 | C4⋊C4 | — | 2 | 1 | no | — |
| 610 | C4⋊C4 | — | 2 | 1 | no | — |
| 611 | C4⋊C4 | — | 2 | 2 | no | — |
| 612 | C4⋊C4 | — | 2 | 2 | no | — |
| 613 | C4⋊C4 | — | 4 | 1 | no | — |
| 614 | C4⋊C4 | — | 4 | 1 | no | — |
| 615 | C4⋊C4 | — | 53 | 1 | no | — |
| 616 | C4⋊C4 | — | 53 | 1 | no | — |
| 617 | C4⋊C4 | — | 106 | 1 | no | — |
| 618 | C4⋊C4 | — | 106 | 1 | no | — |
| 619 | C4⋊C4 | — | 106 | 1 | no | — |
| 620 | C4⋊C4 | — | 106 | 1 | no | — |
| 621 | C4⋊C4 | — | 106 | 1 | no | — |
| 622 | C4⋊C4 | — | 106 | 1 | no | — |
| 623 | C4⋊C4 | — | 106 | 1 | no | — |
| 624 | C4⋊C4 | — | 106 | 1 | no | — |
| 625 | C4⋊C4 | — | 106 | 1 | no | — |
| 626 | C4⋊C4 | — | 106 | 1 | no | — |
| 627 | C4⋊C4 | — | 106 | 1 | no | — |
| 628 | C4⋊C4 | — | 106 | 1 | no | — |
| 629 | C4⋊C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 630 | C4⋊C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 631 | C22⋊C4 | — | 2 | 1 | no | — |
| 632 | C22⋊C4 | — | 2 | 1 | no | — |
| 633 | C22⋊C4 | — | 2 | 1 | no | — |
| 634 | C22⋊C4 | — | 2 | 1 | no | — |
| 635 | C22⋊C4 | — | 2 | 1 | no | — |
| 636 | C22⋊C4 | — | 106 | 1 | no | — |
| 637 | C22⋊C4 | — | 106 | 1 | no | — |
| 638 | C22⋊C4 | — | 106 | 1 | no | — |
| 639 | C22⋊C4 | — | 106 | 1 | no | — |
| 640 | C22⋊C4 | — | 106 | 1 | no | — |
| 641 | C22⋊C4 | — | 106 | 1 | no | — |
| 642 | C22⋊C4 | — | 106 | 1 | no | — |
| 643 | C22⋊C4 | — | 106 | 1 | no | — |
| 644 | C22⋊C4 | — | 106 | 1 | no | — |
| 645 | C22⋊C4 | — | 106 | 1 | no | — |
| 646 | C22⋊C4 | — | 106 | 1 | no | — |
| 647 | C22⋊C4 | — | 106 | 1 | no | — |
| 648 | C22⋊C4 | — | 106 | 1 | no | — |
| 649 | C22⋊C4 | — | 106 | 1 | no | — |
| 650 | C22⋊C4 | — | 106 | 1 | no | — |
| 651 | C22⋊C4 | — | 106 | 1 | no | — |
| 652 | C22⋊C4 | — | 106 | 1 | no | — |
| 653 | C22⋊C4 | — | 106 | 1 | no | — |
| 654 | C22⋊C4 | — | 106 | 1 | no | — |
| 655 | C42 | — | 2 | 1 | no | — |
| 656 | C42 | — | 106 | 1 | no | — |
| 657 | C42 | — | 106 | 1 | no | — |
| 658 | C42 | — | 106 | 1 | no | — |
| 659 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 660 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 661 | C42 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 662 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 663 | C23 | — | 2 | 1 | no | — |
| 664 | C23 | — | 106 | 1 | no | — |
| 665 | C23 | — | 106 | 1 | no | — |
| 666 | C23 | — | 106 | 1 | no | — |
| 667 | C23 | — | 424 | 1 | no | — |
| 668 | C23 | — | 424 | 1 | no | — |
| 669 | C23 | — | 424 | 1 | no | — |
| 670 | C23 | #13133185 | 1 | 1 | yes | characteristic |
| 671 | Q8 | — | 4 | 1 | no | — |
| 672 | Q8 | — | 4 | 2 | no | — |
| 673 | Q8 | — | 4 | 2 | no | — |
| 674 | Q8 | — | 8 | 2 | no | — |
| 675 | Q8 | — | 424 | 1 | no | — |
| 676 | Q8 | — | 212 | 1 | no | — |
| 677 | Q8 | — | 212 | 1 | no | — |
| 678 | Q8 | — | 212 | 1 | no | — |
| 679 | D4 | — | 4 | 1 | no | — |
| 680 | D4 | — | 8 | 1 | no | — |
| 681 | D4 | — | 424 | 1 | no | — |
| 682 | D4 | — | 424 | 1 | no | — |
| 683 | D4 | — | 424 | 1 | no | — |
| 684 | D4 | — | 424 | 1 | no | — |
| 685 | D4 | — | 424 | 1 | no | — |
| 686 | D4 | — | 424 | 1 | no | — |
| 687 | D4 | — | 424 | 1 | no | — |
| 688 | D4 | — | 424 | 1 | no | — |
| 689 | D4 | — | 424 | 1 | no | — |
| 690 | D4 | — | 424 | 1 | no | — |
| 691 | D4 | — | 424 | 1 | no | — |
| 692 | D4 | — | 424 | 1 | no | — |
| 693 | D4 | — | 212 | 1 | no | — |
| 694 | D4 | — | 212 | 1 | no | — |
| 695 | D4 | — | 212 | 1 | no | — |
| 696 | C2×C4 | — | 2 | 2 | no | — |
| 697 | C2×C4 | — | 2 | 1 | no | — |
| 698 | C2×C4 | — | 2 | 1 | no | — |
| 699 | C2×C4 | — | 2 | 1 | no | — |
| 700 | C2×C4 | — | 4 | 1 | no | — |
| 701 | C2×C4 | — | 4 | 1 | no | — |
| 702 | C2×C4 | — | 4 | 2 | no | — |
| 703 | C2×C4 | — | 4 | 2 | no | — |
| 704 | C2×C4 | — | 8 | 2 | no | — |
| 705 | C2×C4 | — | 106 | 1 | no | — |
| 706 | C2×C4 | — | 106 | 1 | no | — |
| 707 | C2×C4 | — | 106 | 1 | no | — |
| 708 | C2×C4 | — | 106 | 1 | no | — |
| 709 | C2×C4 | — | 106 | 1 | no | — |
| 710 | C2×C4 | — | 424 | 1 | no | — |
| 711 | C2×C4 | — | 424 | 1 | no | — |
| 712 | C2×C4 | — | 424 | 1 | no | — |
| 713 | C2×C4 | — | 424 | 1 | no | — |
| 714 | C2×C4 | — | 424 | 1 | no | — |
| 715 | C2×C4 | — | 212 | 2 | no | — |
| 716 | C2×C4 | — | 212 | 2 | no | — |
| 717 | C2×C4 | — | 212 | 2 | no | — |
| 718 | C2×C4 | #13133185 | 1 | 1 | yes | characteristic |
| 719 | C2×C4 | #13133185 | 1 | 1 | yes | characteristic |
| 720 | C2×C4 | #13133185 | 1 | 1 | yes | characteristic |
| 721 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 722 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 723 | C2×C4 | C22×C22⋊D53 | 1 | 1 | yes | characteristic |
| 724 | C8 | — | 4 | 2 | no | — |
| 725 | C8 | — | 212 | 2 | no | — |
| 726 | C8 | — | 212 | 2 | no | — |
| 727 | C22 | — | 2 | 1 | no | — |
| 728 | C22 | — | 2 | 1 | no | — |
| 729 | C22 | — | 2 | 1 | no | — |
| 730 | C22 | — | 4 | 1 | no | — |
| 731 | C22 | — | 4 | 1 | no | — |
| 732 | C22 | — | 4 | 1 | no | — |
| 733 | C22 | — | 424 | 4 | no | — |
| 734 | C22 | — | 212 | 1 | no | — |
| 735 | C22 | — | 212 | 1 | no | — |
| 736 | C22 | — | 212 | 1 | no | — |
| 737 | C22 | — | 212 | 1 | no | — |
| 738 | C22 | — | 212 | 1 | no | — |
| 739 | C22 | — | 212 | 1 | no | — |
| 740 | C22 | — | 212 | 1 | no | — |
| 741 | C22 | — | 212 | 1 | no | — |
| 742 | C22 | — | 212 | 1 | no | — |
| 743 | C22 | C2×#13133185 | 1 | 1 | yes | characteristic |
| 744 | C4 | — | 2 | 1 | no | — |
| 745 | C4 | — | 2 | 1 | no | — |
| 746 | C4 | — | 2 | 1 | no | — |
| 747 | C4 | — | 2 | 1 | no | — |
| 748 | C4 | — | 2 | 1 | no | — |
| 749 | C4 | — | 4 | 1 | no | — |
| 750 | C4 | — | 4 | 1 | no | — |
| 751 | C4 | — | 4 | 1 | no | — |
| 752 | C4 | — | 8 | 2 | no | — |
| 753 | C4 | — | 212 | 1 | no | — |
| 754 | C4 | — | 212 | 1 | no | — |
| 755 | C4 | — | 212 | 1 | no | — |
| 756 | C4 | — | 212 | 1 | no | — |
| 757 | C4 | — | 212 | 1 | no | — |
| 758 | C4 | #16810799 | 1 | 2 | yes | — |
| 759 | C2 | — | 4 | 1 | no | — |
| 760 | C2 | — | 8 | 1 | no | — |
| 761 | C2 | — | 424 | 1 | no | — |
| 762 | C2 | — | 424 | 1 | no | — |
| 763 | C2 | — | 424 | 1 | no | — |
| 764 | C2 | C2×#16810799 | 1 | 1 | yes | characteristic |
| 765 | C2 | #20284086 | 1 | 1 | yes | characteristic |
| 766 | C2 | #20284091 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20285936 | C2 | semidirect |
| 3. #20285111 | C2 | semidirect |
| 4. #20274046 | C2 | semidirect |
| 5. #20274036 | C2 | semidirect |
| 6. #20274029 | C2 | semidirect |
| 7. #20274019 | C2 | semidirect |
| 8. #20273349 | C2 | semidirect |
| 9. #20273323 | C2 | semidirect |
| 10. #20273322 | C2 | semidirect |
| 11. C53×#3218 | C2 | semidirect |
| 30. #16811029 | C22 | semidirect |
| 33. #16810985 | C22 | semidirect |
| 40. #16810680 | C22 | semidirect |
| 43. C4×#11719917 | C22 | semidirect |
| 44. #16810365 | C22 | semidirect |
| 45. #16810364 | C22 | semidirect |
| 49. #16810362 | C22 | semidirect |
| 50. C2×C4⋊Q8×C53 | C22 | semidirect |
| 53. C53×#491 | C22 | semidirect |
| 58. C53×#432 | C22 | semidirect |
| 378. #3218 | D53 | semidirect |
| 407. C2×C4⋊Q8 | C2×D53 | semidirect |
| 417. #491 | C2×D53 | semidirect |
| 432. #432 | C2×D53 | semidirect |
| 442. C53 | #19000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288854 | 2 |
| #20285936 | 2 |
| #20285111 | 2 |
| #20274046 | 2 |
| #20274036 | 2 |
| #20274029 | 2 |
| #20274019 | 2 |
| #20273349 | 2 |
| #20273323 | 2 |
| #20273322 | 2 |
| C53×#3218 | 2 |
| #19000 | 53 |